Problem: Rewrite as a simplified fraction. ${2.3\overline{14} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2314.1414...\\ 10x &= 23.1414...\end{align*}}$ Subtracting the two equations, we have: ${990x = 2291}$ ${x = \dfrac{2291}{990}} \text{or} {2 \dfrac{311}{990}}$